Energy influx from an rf plasma to a substrate during plasma processing

Energy influx from an rf plasma to a substrate during plasma

processing

Citation for published version (APA):

Kersten, H., Stoffels - Adamowicz, E., Stoffels, W. W., Otte, M., Csambal, C., Deutsch, H., & Hippler, R. (2000). Energy influx from an rf plasma to a substrate during plasma processing. Journal of Applied Physics, 87(8), 3637-3645. https://doi.org/10.1063/1.372393

DOI:

10.1063/1.372393

Document status and date: Published: 01/01/2000 Document Version:

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Energy influx from an rf plasma to a substrate during plasma processing

Institute for Physics, University of Greifswald, Domstrasse 10a, D-17487 Greifswald, Germany

E. Stoffels and W. W. Stoffels

Department of Physics, TU Eindhoven, P.O. Box 513, 5600MB Eindhoven, The Netherlands

M. Otte, C. Csambal, H. Deutsch, and R. Hippler

Institue for Physics, University of Greifswald, Domstrasse 10a, D-17487 Greifswald, Germany 共Received 19 July 1999; accepted for publication 18 January 2000兲

The energy influx delivered by an rf plasma to a metal substrate has been studied by a calorimetric method with a thermal probe. By changing the substrate voltage, the influence of the kinetic energy of the charge carriers to the thermal power could be determined. The measured energy influx for an argon plasma can be explained mainly by ions, electrons, and their recombination. In the case of an oxygen plasma, where the energy influx is under comparable conditions about 50% higher, also other transfer mechanisms such as surface-aided atom association and relaxation of rovibrational states have to be taken into consideration. © 2000 American Institute of Physics.

关S0021-8979共00兲05608-5兴

I. INTRODUCTION

Plasma wall interactions are of great importance in a large variety of applications of temperature, low-pressure plasmas such as in etching, deposition, and surface modification of thin films. In these complex processes, the thermal and energetic conditions at the substrate surface play a dominant role.

The thermal conditions at the substrate surface affect elementary processes like adsorption, desorption, and diffu-sion as well as chemical reactions共chemical sputtering, sur-face film reaction兲.1–3 On the other hand, especially in the case of thin film deposition, the microstructure and morphol-ogy as well as the stoichiometry of the film depend strongly on the energetic conditions at the surface.4,5 Also, surface diffusion of adsorbed atoms can be enhanced, which results in a rearrangement of deposited atoms.6 In addition, bom-bardment of a growing film with low-energy ions results in a modification of film properties such as adhesion and residual stress, etc.7

It should be emphasized that in addition to external heat-ing, the surface temperature TS is largely influenced by the

energy flux Jin resulting from energetic particle

bombard-ment, chemical surface reactions and heat radiation.8,9By a suitable variation of the experimental conditions, the differ-ent contributions to the substrate heating can be separated and independently studied.

In the present article, we perform investigations on the energy influx共thermal power兲 to substrates in rather weak rf discharges. In this type of discharge, used for deposition of coatings, cleaning, and conditioning of surfaces, the heat load on the surface is often a critical parameter. Also the heat load of microdisperse powder particles, suspended in a dis-charge is a topic under current investigation.10,11In Sec. II, the various heat sources and sinks of a substrate in a

dis-charge will be discussed. In Sec. III, the design of our ther-mal probe is discussed along with the plasma setup. Mea-surements of the relevant plasma parameters like the electron density and temperature are presented to allow for a good comparison of the measured and calculated heat fluxes, which is shown in the final section.

II. THEORY

When a solid comes into contact with a plasma, energy transfer takes place. The substrate is heated and, after a cer-tain time, it may reach a thermal equilibrium. This steady state is determined by a balance of energy gain from the plasma processes and energy losses by conduction and radiation.12,13 The general power balance at the substrate is given by

Qin⫽H˙S⫹Qout, 共1兲

where H˙S⫽mc(dTS/dt) denotes the enthalpy of the

sub-strate and Qout summarizes the heat losses by radiation and

thermal conduction by the gas and the substrate. For most substrates thermal conduction to共or from, in case of a heated substrate兲 the substrate holder will be the dominant heat sink

共source兲. However, in case of an isolated substrate, like a

trapped microdisperse particle floating in the discharge, this is completely absent. In those cases, radiation and gas cool-ing are the only heat sinks. As we operate at low pressures and low temperatures, both are relatively ineffective and thus the temperature of a thermally isolated object in a discharge can be elevated with respect to its surroundings.10

In the following, the different contributions to the total energy influx Qinwhich are relevant under our experimental

conditions will be discussed shortly. It should be mentioned that the flux Qin is the surface integral of the related energy

flux density Jinover the substrate surface AS: a兲_{Electronic mail: kersten@physik.uni-greifswald.de}

3637

Qin⫽

冕

J_indA. 共2兲

In general, the total energy influx Jin is the sum of the

fluxes due to electrons (Je), ions (Ji), neutrals (Jn), and

photons (Jphot). Each of these fluxes consists of several

con-tributions. The electrons and ions hitting a substrate transfer their kinetic energy, moreover recombination energy is re-leased when a positive ion and electron recombine at the surface. In our case with cold gas and cold substrates, the kinetic energy of neutrals can be neglected, but neutrals can transfer internal energy from electronic and rovibrational ex-citation (J_inter). Furthermore gas molecules can associate with another gas phase species at the surface (J_ass) or react with the surface (J_chem). Heating by photons can occur by blackbody radiation from heated surfaces or by plasma pro-duced photons. In our case, there are no heated surfaces and the metal substrate reflects virtually all photons in the visible region. At our operating pressure and power, the plasma is optically dense for resonant radiation and therefore the ther-mal load of UV photons hitting the substrate is also negli-gible. Note that this is not necessarily true in other plasma configurations or in case of opaque, nonreflecting substrates. Concluding, the total heat influx is given by

Jin⫽Je⫹Jion⫹Jinter⫹Jass⫹Jchem. 共3兲

In the following, we shall estimate these contributions in more detail. In general, the mean kinetic ion energy is deter-mined by the ion energy distribution function 共IEDF兲 at the surface. At elevated pressures, the energy distribution of the ions arriving at the substrate is affected by collisions in the sheath in front of the substrate. At low pressures in the present experiment共1 Pa兲, the maximum ion energy is deter-mined mainly by the free fall energy e0Vbias, where Vbiasis

the potential drop from the plasma glow to the substrate which corresponds to the difference between the plasma po-tential Vpl and the substrate potential VS with respect to

ground:

Vbias⫽Vpl⫺VS. 共4兲

It should be emphasized that the simple expression of Eq. 共4兲 for the mean kinetic energy of the ions striking the substrate is applicable in most cases of plasma processing. Only if the IEDF for the ions near the substrate is much more complex, the assumption of e₀V_biasfor the kinetic energy is no longer justified. In an argon discharge, charge transfer reactions readily occur in the sheath region. In this case, part of the ion energy (e0Vbias) is transferred to a neutral.

How-ever, as the neutral has a directional velocity towards the substrate, still most energy will be transferred to the sub-strate and the simple expression of Eq.共4兲 holds. In addition to the directed kinetic energy of the ions, which originates from acceleration in the electrical field in front of the sub-strate, the ions also have thermal energy. However, this part can be neglected because the ions are nearly at room tem-perature. Hence, the contribution of the kinetic energy of the ions (J_ikin) which can be expressed as a product of the ion flux density ji and their mean energy Ei is given by

Ji kin_{⫽ j} iEi⫽ jie0共Vpl⫺VS兲 ⫽nevambe0共Vpl⫺VS兲 ⫽ne

冑

where we have approximated the ambipolar diffusion nevamb

in Eq.共5兲 by the Bohm flux14

j_i⫽n_e

冑

exp兵⫺0.5其. 共6兲

Under low-pressure conditions ( p⬍10 Pa), the Bohm equation is applicable for argon discharges, because in the presheath almost no collisions occur. The Bohm equation yields the ion flux ji by knowing the ion density ni, which

equals the electron density ne at the sheath edge. This

ap-proach is also valid in presence of negative ions, like in an oxygen discharge. However, in that case the Bohm flux关Eq.

共6兲兴 is governed by the ion temperature.15

In addition to kinetic energy, ions transfer a part of their potential energy when striking a surface. For metallic sub-strates, the neutralization of ions is caused by long-range interactions and may be accompanied by the emission of secondary electrons. The resulting contribution J_irec to the energy balance of the substrate due to the recombination is

J_irec⫽ jiErec. 共7兲

Each incident ion releases its ionization potential Eion

minus the work function of the metal⌽, as an electron has to be released from the metal surface before recombination. In case of secondary electron emission, also their work function has to be supplied. The released recombination energy Erecis

given by

Erec⫽Eion⫺⌽. 共8兲

Data for Eionand⌽, respectively, may be taken from the

literature.16 In principle, Eq.共8兲 should still be corrected by the difference between the adsorption energy of the ion and the desorption energy of the resulting neutral, but this con-tribution is rather low. As stated above, it is assumed that the resulting neutral is in its ground state, especially for molecu-lar ions, this is not necessarily true and appropriate changes in Eion should be made in this case.

The cooling effect by sputtering of substrate material can also be ignored. Because in our case, the energy e0Vbiasof

the impinging ions is always smaller than 100 eV, the sputter yield Y is rather small (Y⭐0.1). Therefore, the flux of sput-tered surface atoms, which may contribute to an energy loss of the substrate, is negligible.

The electrons have to overcome the bias voltage V_biasin front of the substrate in order to reach the substrate surface and to transfer their energy. The kinetic energy of the plasma electrons arises from the integration over the EEDF from

Vbiasup to infinity. Moreover, every electron hitting the

sur-face will release an energy equivalent to the work function of the material. In case of a Maxwellian electron energy distri-bution 共EEDF兲, the energetic influx Jethus reads

Je⫽ne

冑

再

冎

The energy, which the electrons lose by overcoming the bias potential, is stored as potential energy in the electric field and consumed by accelerating ions hitting the substrate and by secondary electrons accelerated towards the plasma. This effect is taken into account by the work function ⌽ in Eq. 共8兲. Both summands of the electron energy 共2kT_e, ⌽兲 are of the same order of magnitude.

Using the general equations 共4兲–共9兲 listed above, an analysis of the charged plasma components will yield, in principle, the surface heating caused by positive ions and electrons. In case of electronegative plasmas like oxygen, negative ions also have to be considered. Because of their low temperature, they can only reach the substrate if there is a large positive bias. Therefore, in general, negative ions can be neglected in the thermal balance of a substrate. As the energy flux of the charged species strongly depends on the bias potential of the substrate关Eqs. 共5兲 and 共9兲兴, it is possible to separate their contribution from other heat sources like radiation, chemical reactions, neutrals, and charge carriers, by variation of the bias potential.

The contribution of the various neutral gas components strongly depends on the gas composition and the plasma con-ditions. In a process plasma containing reactive species 共 N2,O2, etc.兲, surface-aided atomic association and

heteroge-neous exothermic reactions occur. Evidence for substrate heating by exothermic reactions on the processed surface has been reported, for example, in case of plasma etching of silicon with fluorine containing compounds17 and during plasma cleaning of contaminated metal surfaces.18 In the case of atomic recombination as a special surface reaction process, the fraction of the energy transferred to the solid has been described for example in Ref. 19. The percentage of the recombination energy, which is used for surface heating, var-ies with the chemical composition of the surface. Further-more, relaxation of internal energy 共electronic and rovibra-tional excitations兲 adds to the thermal influx to a substrate. Energy transfer of argon metastable atoms and rovibra-tionally excited molecular species to microdisperse particles floating in the discharge has been suggested by Stoffels and Stoffels.20

The energy influx by internal energy transfer Jinter, atom

recombination Jass and exothermic reactions Jchem is

de-scribed by

Jass⫽ jO⌫OEdiss⫽⌫O1

2nO

冑

␲mO

Ediss, 共10兲

in which ⌫ is the energy transfer, association, or reaction probability of the neutrals on the substrate surface and j its flux density. The latter can be determined accurately, if the species density and its diffusion properties are known.21The index O indicates the quantities for oxygen. At low pres-sures, a rough estimate is obtained by simply multiplying the global species density n with its thermal velocity v: j

⫽nv.

If the chemical reactions result in layer formation, one can easily estimate Jchemfrom the growth rate Rdep, the mass

density␳of the layer, and the average specific enthalpy gain

hox.

Jchem⫽Rdep␳h_ox. 共11兲

Analogous formulas can be easily derived in case of etching a substrate, in which the reaction products are volatile.

The thermal load on a substrate resulting from plasma photons can be calculated by integrating the product of pho-ton flux⌽pl(␯), photon energy hv, and absorption coefficient of the surface A(h␯) over the complete spectral range.

Jphot⫽

冕

The photon flux has to be estimated using a radiative plasma model.

The different energetic contributions calculated on the basis of the equations mentioned above can be compared with the total energy influx Jin measured by the probe

method described below. This comparison gives insight into the processes involved and about the dominant mechanisms determining the thermal balance of a substrate during rf plasma treatment.

III. EXPERIMENT

A. Energy flux measurements by a thermal probe The integral energy influx from the plasma towards the substrate can be measured by a simple thermal probe.22 Pre-viously, Thornton23and Wendt et al.24have proposed a simi-lar procedure for the determination of the total heat influx. A schematic sketch of the setup is shown in Fig. 1. The probe is mounted on a manipulator arm to allow for horizontal and vertical scans. It can be also rotated, in order to measure directional fluxes, e.g., secondary electrons coming from an rf electrode or infrared photons from a heated surface.

In our experiments, the heat flux measurements are car-ried out by observing the rate of temperature rise dTS/dt of

a copper substrate 共diameter: 3.4 cm, area AS⫽18 cm2,

thickness: 0.02 cm兲 which is spot welded to a thermocouple

共type j兲 and placed within a solid shield. The substrate is

only connected to the thermocouple and a wire for additional biasing. No other contact to the shield and holder is realized

in order to minimize thermal conduction. Because of its large heat capacity the shield is at a constant environmental tem-perature Tenvduring the time of the measurement.

The measurement of the total energy influx Qinis based

on the determination of the difference between the time de-rivatives of the substrate temperature Ts during heating 共‘‘plasma on’’兲 and cooling 共‘‘plasma off’’兲. Examples of

typical temperature curves TS(t) which have been obtained

for an Ar plasma ( p⫽1 Pa,P⫽15 W) at three different sub-strate voltages are presented in Fig. 2.

The general power balance at the substrate is given by Eq. 共1兲. The losses are always small in comparison to the incoming fluxes due to the plasma process. During the heat-ing phase 共plasma on: Qin⬎0兲 H˙S is determined by H˙S共heat兲⫽Qin⫺Qout and during the cooling phase 共plasma

off: Qin⫽0兲 by H˙S共cool兲⫽⫺Qout. By taking these

expres-sions into Eq. 共1兲, the difference yields the energy influx:

Qin⫽H˙_S共heat兲⫺H˙_S共cool兲⫽mc

再

冉

冊

冉

冊

冎

If the slopes dTS/dt are determined at the same temperature T and assuming no change of the environmental temperature Tenv, which is achieved by short measurement times, the

expression within the brackets of Eq.共13兲 is a quantity pro-portional to the thermal power at the substrate. In order to obtain absolute values of Qin, the specific heat of the

sub-strate 共thermal probe兲 was determined by a known thermal power as described in Ref. 25 to CS⫽0.65 J/K.

The measured energy influx is an integral value compris-ing the various contributions as kinetic energy of charge car-riers, recombination heat, reaction heat, etc. By measuring the energy fluxes at different substrate voltages V_S, the con-tributions of ions and electrons from the other sources can be separated. For this purpose, the thermal probe共substrate兲 can be biased externally by a dc voltage. Simultaneously, the electrical current to the substrate is measured and one obtains the substrate characteristic, which is similar to a usual probe characteristic. In Fig. 3, the thermal probe characteristic in an 1 Pa argon and oxygen rf plasma is shown. At sufficiently negative substrate voltages, the current IS changes only

slightly with increasing voltage VS. From the characteristics

in Fig. 3, an ion saturation current of about 1 mA and a floating potential of Vfl⬇⫺3 V can be obtained for the argon plasma.

B. The plasma setup

In order to test the thermal probe, a commonly used asymmetric, capacitively coupled rf discharge was used. The plasma glow is located in the region between the plane alu-minum rf electrode (D⫽130 mm) and the upper part of the spherically shaped reactor vessel (D⫽400 mm) which serves as grounded electrode, see Fig. 1.

The 13.56 MHz rf power is supplied by a generator

共Dressler CESAR1310兲 in combination with an automatic

matching network 共Dressler VM700兲. The rf voltage was varied between 300 and 900 V, resulting in a discharge power of 10–100 W. The turbopump 共Pfeiffer TMU260C兲 which allows for a base pressure of 10⫺4Pa is connected to the vessel by a butterfly valve, the gas pressure was varied between 0.5 and 5 Pa by the valve and by using a flow controller 共MKS兲. Argon and oxygen, respectively, were used as process gases.

C. Plasma diagnostics

In order to compare the measured energy fluxes with simple model assumptions, the internal plasma parameters of the rf discharge have been investigated by plasma diagnos-tics as analytical charge coupled device 共CCD兲 photometry and Langmuir-probe measurements,26 respectively.

A CCD camera共SBIG ST-6兲 coupled with a photoelec-trical filter共CRI VIS2-05兲 was used to determine the sheath width in front of the powered electrode by measuring the spatial emission profile at several wavelengths. This gives information on the local variations in the electron energy distribution function, with a high spatial accuracy共0.2 mm兲. The Langmuir-probe characteristics have been obtained by a source meter共Keithley SM2400兲. The probe 共diameter: 47␮m, length: 12 mm兲 could be moved axially through the plasma bulk into the plasma glow near the sheath, see Fig. 1. During a measurement, the probe voltage is stepwise in-creased and the electrical probe current is recorded from the

FIG. 2. TS(t) curves as measured during the Ar plasma process

( p⫽1 Pa,P⫽15 W) for three substrate voltages 共0, ⫺46, ⫺95 V兲.

FIG. 3. Current–voltage characteristic of the substrate共thermal probe兲 for

argon and oxygen.

ion acceleration region up to the electron acceleration region. The electron energy distribution function 共EEDF兲 can then directly be determined from the second derivative of the V – I characteristics.27 Figure 4 shows examples for the second derivative for argon at 0.75 Pa and 10 W taken at several distances above the electrode which yield Maxwellian distri-butions. The values of the electron density neand the mean

electron energy ue(kTe) as well as the plasma and floating

potentials (Vpl,Vfl) have been determined from the probe’s

current–voltage characteristics.

IV. RESULTS AND DISCUSSION A. Plasma parameters

The interpretation of the substrate heating by charge car-riers requires the determination of the electron and ion den-sity (ne,ni), the plasma and the floating potential (Vpl,Vfl),

and the electron temperature (kTe). In the present study, the

internal plasma parameters have been measured in the sub-strate region by analytical CCD photometry and Langmuir-probe measurements as described above.

The sheath position has been determined by the CCD photometry technique. For example, the extension of the sheath thickness dshfor an argon plasma has been estimated

for two different excitation levels at 420 nm (1s5– 3 p9) and

668 nm (1s4– 2 p1). Figure 5 shows an example of the

mea-sured sheath width d_shfor p⫽1 Pa in dependence on the rf power. The accuracy of the determination of d_shis⫾0.2 mm. Since the required energy for the excitation of the 2 p level

共13.48 eV兲 is lower than the excitation energy for the 3p

level共14.5 eV兲, the glow in the 668 nm line can be observed closer to the electrode. This observation, which is known as Seeliger’s rule of glow edge,28is due to the kinetic energy of ␥electrons originating from the electrode and accelerated in the sheath. The larger the distance from the electrode, the more kinetic energy the electrons gain for exciting collisions. In Fig. 5, the sheath widths measured by the CCD method are also compared with values obtained by

Langmuir-probe measurements. In this case, dshwas defined

as the distance from the electrode where the V – I character-istic of the Langmuir-probe failed. This means that within a distance of about 20 mm in front of the electrode 共sheath兲, the second derivative of the probe characteristic, which is needed to determine the EEDF as well as the electron density and the electron temperature, is strongly disturbed and an evaluation of the probe characteristic becomes impossible. Both methods yield reliable values for the sheath thick-nesses, but obviously the CCD method is more accurate. In systematic measurements, a weak dependence on the dis-charge power共Fig. 5兲, and a strong influence of the pressure on dshcould be observed. In all cases the sheath thickness is

in the order of a centimeter.

In addition, by using a balance equation,29 the internal plasma parameters for an Ar plasma could also be obtained. Under the assumption that charge carrier formation occurs mainly by direct impact ionization within the plasma glow and by measuring the external discharge quantities as the amplitude of the rf voltage (Vpp⬃Vrf), the dc-bias voltage (Vdc) and the sheath thickness in front of the hot electrode,

the model yields the electron temperature kTe and electron

density ne.

The floating potential is Vfl⫽⫺3 V and the plasma po-tential Vplis in the order of 15 V for argon and about 20 V

for oxygen plasma, respectively. The plasma potential changes only slightly within the plasma glow. Figure 6 shows the variation of the plasma potential in an argon plasma as a function of the axial distance from the rf elec-trode. As mentioned above, the position where the potential drops dramatically and the evaluation of the EEDF fails can be identified as the sheath edge and it coincides with the optically determined sheath edge position 共Fig. 5兲. A quite similar behavior can be observed in the axially measured electron temperature, shown in Fig. 7. At the sheath edge, there are hardly any electrons from the plasma glow. Most electrons are secondary electrons, heated in the sheath re-gion. Thus, kTe increases strongly towards the rf electrode,

while the electron density ne drops. The values at substrate

position共3.25 cm兲, which are important for the calculations, are 3.5 eV for the argon plasma and about 5.2 eV for the

FIG. 4. Second derivative of Langmuir-probe characteristics, which is a measure for the EEDF obtained at different heights above the rf electrode ( p⫽0.75 Pa,P⫽10 W).

FIG. 5. Observed sheath thickness dshin front of the rf electrode for two

wavelengths and determined by a Langmuir-probe for different rf power. The argon gas pressure was 1 Pa.

oxygen plasma. For a Maxwellian EEDF, the electron tem-perature can also be simply estimated by the difference be-tween floating and plasma potential:

Vfl⫺Vpl⫽kTe

2e0

ln

冉

mi

冊

⭐0. 共14兲

This formula yields for argon (Vfl⫺Vpl⫽⫺18 V,me/mi ⫽1.4⫻10⫺5_{), an electron temperature of 3.5 eV. By using}

the relevant values for oxygen, one obtains kT_e⫽4.6 eV. Comparison with the measurement supports the assumption of a Maxwellian EEDF at least for the argon plasma.

The electron density n_e for argon at a power of 15 W and a pressure of 1 Pa, which were the standard discharge conditions in energy flux measurements, is about 2

⫻109_{cm⫺3共Fig. 8兲. The values for the electron density and}

their dependence on discharge power determined by the Langmuir-probe measurements are also confirmed by the op-tical measurements on the basis of the sheath model.

B. Argon plasma

In the case of an argon plasma, we will initially consider the energetic contributions due to kinetic energy of the charge carriers 关Eqs. 共5兲 and 共9兲兴 and their recombination

关Eq. 共7兲兴. The contributions of the inert gas are limited, as

there are no association and chemical reactions at the sub-strate surface. Only transfer of internal energy has to be con-sidered.

In order to model Je and Ji the internal plasma

param-eters obtained by Langmuir-probe measurements have been taken. The quantities are calculated for different substrate voltages V_S. The results are plotted in Fig. 9. It is obvious that for V_S⬍Vfl, only the positive ions dominate the integral energy influx Qin, while the contribution of electrons

be-comes important for VS⬎Vfl. In the range VS⬎0, Je

in-creases dramatically due to the flux of electrons which is now drained by the substrate25 acting as an additional dis-turbing electrode. Therefore, for positive substrate voltages, the model calculation on the basis of the Langmuir-probe measurements will fail and one should take the electron flux

jewhich can be directly obtained from the substrate

charac-teristic共Fig. 3兲:

je⫽ I_S e0AS

. 共15兲

The contribution by electrons for VS⬎0 according to this

expression is remarkably smaller than the values one obtains by assuming an undisturbed plasma and applying the

FIG. 6. Axially resolved plasma potential Vplfor an argon rf plasma at 1 Pa. The rf electrode is at z⫽0.

FIG. 7. Axially resolved electron temperature kTefor argon and oxygen

plasma, respectively, at 1 Pa. The sheath edge is at z⫽1.9 cm.

FIG. 8. Electron density nein dependence on axial position z.

FIG. 9. Calculated contributions by ions (Ji,Jrec) and electrons (Je) to the thermal balance of the substrate. The calculations are based on nemeasured by the Langmuir-probe and obtained by the substrate characteristics, respec-tively.

Langmuir-probe measurements. This can be expected be-cause a relatively large, positively biased thermal probe will significantly drain the electrons from the plasma. As a con-sequence, j_e and J_e are lowered.

The energy influx due to charged particles, if both elec-trons and ions are present, can also be estimated from the Bohm flux关Eq. 共6兲兴. Assuming je⫽ ji and remembering that

in this case the electron energy flux can be neglected, the ion energy flux is simply given by Ji⫽ ji(Eion⫹eVbias).

Substi-tuting the electron density and temperature measured using the probe technique (ne⫽2⫻109cm⫺3,kTe⫽3.5 eV) yields

a total ion current to the thermal probe of 0.5 mA, which is in excellent agreement with the measured flux shown in Fig. 3. The total energy flux by ions for Vs⫽Vflto our probe thus

is about 10⫺2J/s, which remarkably agrees well with the extrapolated value for ion heating plotted in Fig. 9.

Finally, the measurements of the total energy influx as a function of the substrate voltage are shown in Fig. 10 for the different VS regions. The influx Qinmeasured by the thermal

probe 共solid squares兲 decreases with increasing substrate voltage in the range VS⬍Vfl, reaches its minimum at VS ⫽Vfl and increases again with the supplied voltage in the range VS⬎Vfl. For sufficiently negative substrate voltages 共left part of the graph兲, the ion saturation current ji towards

the substrate is nearly constant and the deposited thermal power depends only on the ion energy, which is given by the difference between the plasma and substrate potential. If this difference becomes smaller, the contribution J_i decreases. The model, which takes the Bohm criterion and the plasma parameter measured by the Langmuir-probe into account

共open circles兲 reflects the experimentally obtained slope of Jinquite well. The constant difference between the two data

sets reflects the heating by neutrals. The measurements at the right branch that means for positive substrate voltages have been modeled with the electron flux derived from the sub-strate characteristic shown in Fig. 3. In this region, the ions are not important, while the probe model yields electron con-tributions which are much too large.

It can be easily seen that the contribution of neutral spe-cies to the thermal load is about 2⫻10⫺2J/s. In our case, the

contribution of photons can be neglected. The plasma is op-tically dense for resonant photons, so they cannot reach the substrate, while photons in the optical region are reflected as the probe has a metallic surface. The energetic neutral spe-cies in an argon plasma are most likely the argon metastable states. Their density is about 1011cm⫺3.30Indeed, following the estimation given in the theoretical part and assuming a total conversion at the surface, we find the missing thermal load.

Thus, in an argon plasma the integral energy influx Jin

can be determined by a calorimetric method. It consists of the kinetic energy of charge carriers and their recombination energy and the energy released by relaxation of metastables. The contribution of ions (Jion) and electrons (Je) can be

distinguished by a variation of the substrate potential VS.

For practical purposes, a more simple description of the measured curve can be useful by taking

Qin⫽Qin共Vfl兲⫹ISVS, 共16兲

in which Qin(Vfl) denotes the experimentally determined

en-ergy influx at floating potential. By this ‘‘model’’ 共open squares in Fig. 10兲, one can clearly recognize that the whole electric power at the substrate is transferred into thermal power resulting in a certain thermal balance of the substrate. Especially for the ions, this excellent agreement means that the energy accomodation of Ar⫹ions at a metallic surface is close to unity. Recent investigations by Toyoda and Sugai31 show that ion survival at the surface is less than 5%.

The results indicate that a description of the energy in-flux by charge carriers, which are characterized by plasma diagnostics 共probe, substrate兲, is an appropriate method for the treatment of plasma-substrate interaction. Vice versa, by measuring the energy influx with a thermal probe and under the assumption of valid models for the different VS regions,

one can also get some information on the plasma data.

C. Oxygen plasma

The discussion of J_inin case of an oxygen plasma can be given, in principle, in a quite similar manner as it has been done for argon. In an oxygen discharge, there are three main charge carriers, the electrons, the O⫹ ion, and the O⫺ ion. Furthermore, there are several minority species like O₂⫹, O₂⫺, and O₃⫺, which can be ignored in the energy flux balance.21Negative ions also cannot reach the substrate, un-less VSⰇ0, and even in that case their energy is limited.

Therefore, they can be ignored in the flux equations. Never-theless, the presence of negative ions does alter the dis-charge. In most cases, the negative ion density will exceed the electron density thus n_eⰆn_⫹. Moreover, the transport properties and sheath structure are different in an electrone-gative plasma.32Thus, appropriate changes have to be made to Eqs. 共5兲–共9兲.15 This also makes the interpretation of the probe measurements of the plasma parameters more compli-cated.

Nevertheless, treatment of the charged species energy flux is relatively straightforward. An accurate estimate of the neutral species contribution to the energy flux is more com-plex because of the molecular nature of oxygen. Like argon,

FIG. 10. Comparison of measured energy influx Qin with several model

oxygen can be electronically excited. In addition, the oxygen molecules in general will have rovibrational energy. Asso-ciation reactions of oxygen atoms forming oxygen molecules have also to be taken into account. However, the reaction probabilities for rovibrational deexcitation and association on a surface exposed to a discharge are poorly known. Nor is the final state of the reaction products known. In a previous study, these reactions were shown to have a major impact on the plasma characteristics.21Under our conditions, oxidation of the copper probe surface is expected only in the initial stage of probe usage, resulting in the formation of a passi-vating layer. Thus, this term can be neglected, but in general, reactions with the probe surface have also to be considered. The principles of both mechanisms are illustrated by sche-matic reaction graphs in Fig. 11.

As a complete treatment of an oxygen discharge is be-yond the scope of this article, in Fig. 12, we only compare thermal probe measurements of the energy influx to the sub-strate in an O2and an argon plasma under the same

macro-scopic conditions共1 Pa, 15 W, same geometry兲. It is obvious that the total energy influx for oxygen is higher than for argon. The decreased slope for VS⬍0 with respect to argon

indicates that in contrast to argon, in the oxygen plasma the main contribution to the energy flux is caused by neutral species.

V. CONCLUSION

The total energy influx (Jin⫽Qin/AS) from a low power

argon rf plasma共1 Pa, 15 W兲 towards a metal substrate has been determined by a thermal probe to be in the order of 6

⫻10⫺3_{– 3⫻10}⫺3_J/cm2_{s for negative substrate voltages in}

the range of ⫺100–0 V where the ions are the dominant species for surface heating. For positive VS, the flux is in the

order of 3⫻10⫺3– 8⫻10⫺3J/cm2s and the kinetic energy of the electrons is the main source for surface heating. The complete kinetic energy of the charge carriers is transferred into substrate heating. In case of an oxygen rf plasma under the same experimental conditions, the energy influx Jin for VS⫽⫺110– 0 V is in the order of 9⫻10⫺3– 5⫻10⫺3

J/cm2s which is about 50% higher than for argon at the same substrate voltages. In contrast to argon, in oxygen, the main contribution to the energy influx is by neutral species and not by charge carriers. In both cases, the deposited thermal power is rather low in comparison to other plasma processes as sputtering or surface cleaning,18but probably comparable to the thermal load of macroscopic particles suspended in the discharge.11The results underline the sensitivity of the ther-mal probe method and its capability to separate several con-tributions to the total thermal influx.

ACKNOWLEDGMENTS

The work has been supported by the Deutsche For-schungsgemeinschaft 共DFG兲 under SFB198/A14. The au-thors wish to express their thanks to A. Knuth. E.S., and W.W.S. wish to acknowledge the support of the Royal Dutch Academy of Science 共KNAW兲.

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